Numerically Reliable Computation of Characteristic Polynomials
نویسندگان
چکیده
In this paper, we present an algorithm for computing the characteristic polynomial of the pencil (A ? sE). It is shown that after a preliminary reduction of the matrices A and E to, respectively, an upper Hessenberg and an upper triangular matrix, the problem of computing the characteristic polynomial is transformed to the solution of certain triangular systems of linear algebraic equations. We show that the computed characteristic polynomial corresponds exactly to perturbed matrices A + A and E + E and we derive bounds for A and E. We also suggest how to improve on this backward error via iterative reenement.
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